Knudsen number

Knudsen number [kə′nüd·sən ‚nəm·bər]

(fluid mechanics)

The ratio of the mean free path length of the molecules of a fluid to a characteristic length; used to describe the flow of low-density gases.

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Knudsen number

In gas dynamics, the ratio of the molecular mean free path λ to some characteristic length L: Kn = λ/L. The length chosen will depend on the problem under consideration. It may be, for example, the diameter of a pipe or an object immersed in a flow, or the thickness of a boundary layer or a shock wave. See Mean free path

The magnitude of the Knudsen number determines the appropriate gas dynamic regime. When the Knudsen number is small compared to unity, of the order of Kn ≤ 0.1, the fluid can be treated as a continuous medium and described in terms of the macroscopic variables: velocity, density, pressure, and temperature. In the transition flow regime, for Knudsen numbers of the order of unity or greater, a microscopic approach is required, wherein the trajectories of individual representative molecules are considered, and macroscopic variables are obtained from the statistical properties of their motions. In both internal and external flows, for Kn ≥ 10, intermolecular collisions in the region of interest are much less frequent than molecular interactions with solid boundaries, and can be ignored. Flows under such conditions are termed collisionless or free molecular. In the range 0.1 ≤ Kn ≤ 1.0, termed the slip flow regime, it is sometimes possible to obtain useful results by treating the gas as a continuum, but allowing for discontinuities in velocity and temperature at solid boundaries. See Gas dynamics, Kinetic theory of matter, Rarefied gas flow